For most materials that are tested at room temperature, the plastic strain is a function of the applied stress, but not a function of time. At relatively high temperatures 0.5Tm > T > 0.3Tm where Tm is the solidus temperature, metals and ceramics usually begin to exhibit time-dependant plasticity. This type of behavior is called creep, and it is usually the limiting factor in the selection of materials for use at elevated temperatures. Creep is a diffusion-controlled, thermally activated process that results in slow, continuous plastic deformation. For example, suppose we apply a stress of 10,000 psi to a bar made from structural steel and measure the elongation. If we leave the bar under load overnight, there won’t be any significant change in the elongation the following morning. But if we place the same specimen in a furnace at 1000 F and run the experiment again, we would find that there would be a measurable increase in the elongation the next morning. This is because the material creeps at 1000 F. It undergoes slow, continuous plastic deformation. As another example, consider the creep deformation of a turbine blade in a jet engine. If the blades plastically deform under load at operating temperature, then they could elongate enough to strike the walls of the turbine. This would cause them to bend or even fracture, which would result in the loss of power to that engine. Ultimately, this could lead to the crash of an aircraft. This is why creep is so important.
There are in general three stages to creep deformation. During the initial stage, called primary creep, the strain increases rapidly with time. During stage II, called secondary creep, the material enters a steady state and the strain increases steadily with time. During stage III the strain increases rapidly with time until failure occurs. The useful life of a material is usually spent in stage II, so that secondary creep plays a dominant role in determining the lifetime of a component. An empirical formula for the steady state creep rate is given by,
Creep Rate = A*[(stress)^n]*exp{-(Q/RT)}
where A is the creep constant, n is the creep exponent (which usually lies between 3 and 8), Q is the activation energy, R is the universal gas constant, and T is the absolute temperature. If we know A, n, and Q for a specific material, then we can calculate the strain rate at any temperature and stress. For a fixed temperature, this equation represents what is known as power law creep.
There are two distinct mechanisms for creep: dislocation creep and diffusional creep. Both are limited by the rate of atomic diffusion, so both follow an exponential temperature dependence according to Arrhenius’s Law. Dislocations possess the following characteristics:
1.) Except for a few cases, plastic deformation and dislocation motion are mutually inclusive; one cannot occur without the other.
2.) The mobility of a dislocation is affected by two things; the inherent lattice resistance to its motion, and the obstacles that are placed in its path. These obstacles may include hard precipitates and other dislocations.
When a dislocation encounters an obstacle, it slows down. But if the temperature of the material is greater than about 0.3Tm, atoms may diffuse around the obstacle quickly enough to “unlock” the dislocation. This makes it much easier for the dislocation to move past the obstacle. The motion of these “unlocked” dislocations under the applied stress is what leads to dislocation creep.
So how does this happen? When a dislocation encounters a hard precipitate, it can’t glide upwards to clear the obstacle because that would force it out of its slip plane. But if the atoms at the bottom of the half-plane are able to diffuse away, then the net effect is that the dislocation climbs upward. The applied stress acts as a mechanical driving force for this to occur. After the dislocation climbs high enough, it can clear the precipitate and then continue to move along its slip plane. After a short time it will encounter another obstacle, and the whole process repeats itself. This explains the slow, continuous nature of dislocation creep. Does this answer your question?
Maui
